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Numerical Comparison of Controls and Verification of Optimality for Stochastic Control Problems

Author

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  • K. Helmes

    (Humboldt University of Berlin)

  • R. H. Stockbridge

    (University of Kentucky)

Abstract

We provide two approaches to the numerical analysis of stochastic control problems. The analyses rely on linear programming formulations of the control problem and allow numerical comparison between controls and numerical verification of optimality. The formulations characterize the processes through the moments of the induced occupation measures. We deal directly with the processes rather than with some approximation to the processes. Excellent software is readily available, since the computations involve finite-dimensional linear programs.

Suggested Citation

  • K. Helmes & R. H. Stockbridge, 2000. "Numerical Comparison of Controls and Verification of Optimality for Stochastic Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 106(1), pages 107-127, July.
    • Handle: RePEc:spr:joptap:v:106:y:2000:i:1:d:10.1023_a:1004659107996
    DOI: 10.1023/A:1004659107996
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    References listed on IDEAS

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    1. Eric V. Denardo, 1970. "On Linear Programming in a Markov Decision Problem," Management Science, INFORMS, vol. 16(5), pages 281-288, January.
    2. Alan S. Manne, 1960. "Linear Programming and Sequential Decisions," Management Science, INFORMS, vol. 6(3), pages 259-267, April.
    3. Cyrus Derman, 1962. "On Sequential Decisions and Markov Chains," Management Science, INFORMS, vol. 9(1), pages 16-24, October.
    4. Philip Wolfe & G. B. Dantzig, 1962. "Linear Programming in a Markov Chain," Operations Research, INFORMS, vol. 10(5), pages 702-710, October.
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    Cited by:

    1. P. Kaczmarek & S. Kent & G. Rus & R. Stockbridge & B. Wade, 2007. "Numerical solution of a long-term average control problem for singular stochastic processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 451-473, December.
    2. Kurt Helmes & Stefan Röhl, 2008. "A Geometrical Characterization of Multidimensional Hausdorff Polytopes with Applications to Exit Time Problems," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 315-326, May.
    3. Melda Ormeci Matoglu & John Vande Vate, 2011. "Drift Control with Changeover Costs," Operations Research, INFORMS, vol. 59(2), pages 427-439, April.

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